Nuprl Lemma : case-term-1
∀[Gamma:j⊢]. ∀[phi:{Gamma ⊢ _:𝔽}]. ∀[A:{Gamma ⊢ _}]. ∀[u:{Gamma ⊢ _:A}]. ∀[v:Top].
Gamma ⊢ (u ∨ v)=u:A supposing phi = 1(𝔽) ∈ {Gamma ⊢ _:𝔽}
Proof
Definitions occuring in Statement :
case-term: (u ∨ v),
same-cubical-term: X ⊢ u=v:A,
face-1: 1(𝔽),
face-type: 𝔽,
cubical-term: {X ⊢ _:A},
cubical-type: {X ⊢ _},
cubical_set: CubicalSet,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
same-cubical-term: X ⊢ u=v:A,
true: True,
guard: {T},
squash: ↓T,
prop: ℙ,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
case-term-equal-left,
thin-context-subset,
context-subset-term-subtype,
face-1_wf,
istype-top,
cubical-term_wf,
cubical-type-cumulativity2,
cubical_set_cumulativity-i-j,
cubical-type_wf,
face-type_wf,
cubical_set_wf,
context-subset_wf,
subset-cubical-term,
context-1-subset,
subtype_rel_wf,
squash_wf,
true_wf,
istype-universe,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
sqequalRule,
axiomEquality,
equalityIstype,
inhabitedIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
universeIsType,
instantiate,
natural_numberEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache,
independent_isectElimination,
lambdaEquality_alt,
imageElimination,
universeEquality,
imageMemberEquality,
baseClosed,
productElimination,
independent_functionElimination
Latex:
\mforall{}[Gamma:j\mvdash{}]. \mforall{}[phi:\{Gamma \mvdash{} \_:\mBbbF{}\}]. \mforall{}[A:\{Gamma \mvdash{} \_\}]. \mforall{}[u:\{Gamma \mvdash{} \_:A\}]. \mforall{}[v:Top].
Gamma \mvdash{} (u \mvee{} v)=u:A supposing phi = 1(\mBbbF{})
Date html generated:
2020_05_20-PM-03_11_30
Last ObjectModification:
2020_04_06-PM-02_01_47
Theory : cubical!type!theory
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