Nuprl Lemma : cc-fst-comp-csm-m-term
∀[H:j⊢]. ∀[phi:{H ⊢ _:𝔽}]. (((phi)p)m = ((phi)p)p ∈ {H.𝕀.𝕀 ⊢ _:𝔽})
Proof
Definitions occuring in Statement :
csm-m: m,
face-type: 𝔽,
interval-type: 𝕀,
cc-fst: p,
cube-context-adjoin: X.A,
csm-ap-term: (t)s,
cubical-term: {X ⊢ _:A},
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
all: ∀x:A. B[x],
guard: {T},
cube-context-adjoin: X.A,
cc-fst: p,
csm-ap-term: (t)s,
csm-m: m,
csm-ap: (s)x,
cc-adjoin-cube: (v;u),
pi1: fst(t),
cubical-term-at: u(a),
bdd-distributive-lattice: BoundedDistributiveLattice,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
so_apply: x[s]
Lemmas referenced :
cubical-term_wf,
face-type_wf,
cubical_set_wf,
cubical-term-equal2,
cube-context-adjoin_wf,
cubical_set_cumulativity-i-j,
interval-type_wf,
csm-ap-term_wf,
csm-face-type,
cc-fst_wf,
I_cube_wf,
fset_wf,
nat_wf,
csm-m_wf,
I_cube_pair_redex_lemma,
lattice-point_wf,
face_lattice_wf,
subtype_rel_set,
bounded-lattice-structure_wf,
lattice-structure_wf,
lattice-axioms_wf,
bounded-lattice-structure-subtype,
bounded-lattice-axioms_wf,
equal_wf,
lattice-meet_wf,
lattice-join_wf,
face-type-at,
cubical-term-at_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
hypothesis,
universeIsType,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
sqequalRule,
isect_memberEquality_alt,
axiomEquality,
isectIsTypeImplies,
inhabitedIsType,
applyEquality,
because_Cache,
Error :memTop,
independent_isectElimination,
lambdaFormation_alt,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
productElimination,
lambdaEquality_alt,
hyp_replacement,
productEquality,
cumulativity,
isectEquality
Latex:
\mforall{}[H:j\mvdash{}]. \mforall{}[phi:\{H \mvdash{} \_:\mBbbF{}\}]. (((phi)p)m = ((phi)p)p)
Date html generated:
2020_05_20-PM-04_42_08
Last ObjectModification:
2020_04_10-AM-11_23_51
Theory : cubical!type!theory
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