Nuprl Lemma : function-eq_wf
∀[A:Type]. ∀[B:Base]. ∀[f,g:Base]. (function-eq(A;a.B[a];f;g) ∈ Type) supposing base-type-family{i:l}(A;a.B[a])
Proof
Definitions occuring in Statement :
function-eq: function-eq(A;a.B[a];f;g),
base-type-family: base-type-family{i:l}(A;a.B[a]),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
base: Base,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
function-eq: function-eq(A;a.B[a];f;g),
so_lambda: λ2x.t[x],
prop: ℙ,
all: ∀x:A. B[x],
so_apply: x[s],
label: ...$L... t
Lemmas referenced :
base-type-family_wf,
equal-wf-base,
isect_wf,
base_wf,
uall_wf,
base-type-family-implies
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
hypothesis,
sqequalRule,
lambdaEquality,
because_Cache,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
baseApply,
closedConclusion,
baseClosed,
axiomEquality,
isect_memberEquality,
cumulativity,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[B:Base].
\mforall{}[f,g:Base]. (function-eq(A;a.B[a];f;g) \mmember{} Type) supposing base-type-family\{i:l\}(A;a.B[a])
Date html generated:
2016_05_13-PM-03_53_29
Last ObjectModification:
2016_01_14-PM-07_15_51
Theory : per!type
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