Nuprl Lemma : copathAgree_refl
∀[A:𝕌']. ∀[B:A ⟶ Type]. ∀[w:coW(A;a.B[a])]. ∀x:copath(a.B[a];w). copathAgree(a.B[a];w;x;x)
Proof
Definitions occuring in Statement :
copathAgree: copathAgree(a.B[a];w;x;y),
copath: copath(a.B[a];w),
coW: coW(A;a.B[a]),
uall: ∀[x:A]. B[x],
so_apply: x[s],
all: ∀x:A. B[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
copath: copath(a.B[a];w),
copathAgree: copathAgree(a.B[a];w;x;y),
nat: ℕ,
member: t ∈ T,
less_than: a < b,
and: P ∧ Q,
less_than': less_than'(a;b),
top: Top,
true: True,
squash: ↓T,
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
top_wf,
less_than_anti-reflexive,
less_than_wf,
coPathAgree_refl,
copath_wf,
coW_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
cut,
setElimination,
rename,
hypothesisEquality,
hypothesis,
because_Cache,
lessCases,
introduction,
sqequalRule,
isectElimination,
sqequalAxiom,
extract_by_obid,
isect_memberEquality,
independent_pairFormation,
voidElimination,
voidEquality,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_functionElimination,
imageElimination,
lambdaEquality,
applyEquality,
dependent_functionElimination,
instantiate,
cumulativity,
functionEquality,
universeEquality
Latex:
\mforall{}[A:\mBbbU{}']. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[w:coW(A;a.B[a])]. \mforall{}x:copath(a.B[a];w). copathAgree(a.B[a];w;x;x)
Date html generated:
2018_07_25-PM-01_40_47
Last ObjectModification:
2018_06_08-PM-06_53_28
Theory : co-recursion
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