Nuprl Lemma : unglue-term-1
∀[Gamma:j⊢]. ∀[A:{Gamma ⊢ _}]. ∀[phi:{Gamma ⊢ _:𝔽}]. ∀[T:{Gamma, phi ⊢ _}]. ∀[w:{Gamma, phi ⊢ _:(T ⟶ A)}].
∀[b:{Gamma ⊢ _:Glue [phi ⊢→ (T;w)] A}].
unglue(b) = app(w; b) ∈ {Gamma ⊢ _:A} supposing phi = 1(𝔽) ∈ {Gamma ⊢ _:𝔽}
Proof
Definitions occuring in Statement :
unglue-term: unglue(b),
glue-type: Glue [phi ⊢→ (T;w)] A,
context-subset: Gamma, phi,
face-1: 1(𝔽),
face-type: 𝔽,
cubical-app: app(w; u),
cubical-fun: (A ⟶ B),
cubical-term: {X ⊢ _:A},
cubical-type: {X ⊢ _},
cubical_set: CubicalSet,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
constrained-cubical-term: {Gamma ⊢ _:A[phi |⟶ t]},
squash: ↓T,
subtype_rel: A ⊆r B,
true: True,
guard: {T},
prop: ℙ,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
unglue-term_wf2,
face-1_wf,
istype-cubical-term,
glue-type_wf,
context-subset_wf,
cubical-fun_wf,
thin-context-subset,
cubical-type_wf,
face-type_wf,
cubical_set_wf,
cubical-type-cumulativity2,
cubical_set_cumulativity-i-j,
cubical-term-eqcd,
subset-cubical-term,
context-1-subset,
subtype_rel_wf,
squash_wf,
true_wf,
istype-universe,
cubical-term_wf,
iff_weakening_equal
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
equalityIstype,
inhabitedIsType,
universeIsType,
instantiate,
applyLambdaEquality,
setElimination,
rename,
sqequalRule,
imageMemberEquality,
baseClosed,
imageElimination,
equalitySymmetry,
applyEquality,
because_Cache,
natural_numberEquality,
equalityTransitivity,
independent_isectElimination,
lambdaEquality_alt,
universeEquality,
productElimination,
independent_functionElimination
Latex:
\mforall{}[Gamma:j\mvdash{}]. \mforall{}[A:\{Gamma \mvdash{} \_\}]. \mforall{}[phi:\{Gamma \mvdash{} \_:\mBbbF{}\}]. \mforall{}[T:\{Gamma, phi \mvdash{} \_\}].
\mforall{}[w:\{Gamma, phi \mvdash{} \_:(T {}\mrightarrow{} A)\}]. \mforall{}[b:\{Gamma \mvdash{} \_:Glue [phi \mvdash{}\mrightarrow{} (T;w)] A\}].
unglue(b) = app(w; b) supposing phi = 1(\mBbbF{})
Date html generated:
2020_05_20-PM-05_46_01
Last ObjectModification:
2020_04_21-PM-07_48_28
Theory : cubical!type!theory
Home
Index