Nuprl Lemma : has-value_functionality
∀[a,b:Base]. {(a)↓ ⇒ (b)↓} supposing a ≤ b
Proof
Definitions occuring in Statement :
has-value: (a)↓,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
guard: {T},
implies: P ⇒ Q,
base: Base,
sqle: s ≤ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
guard: {T},
implies: P ⇒ Q,
has-value: (a)↓,
prop: ℙ,
all: ∀x:A. B[x]
Lemmas referenced :
has-value_wf_base,
sqle_wf_base,
base_wf,
sqle_trans,
cbv-sqequal0,
is-exception_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
sqequalHypSubstitution,
extract_by_obid,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
axiomSqleEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
baseClosed,
baseApply,
closedConclusion,
independent_functionElimination,
divergentSqle,
sqleRule,
independent_isectElimination
Latex:
\mforall{}[a,b:Base]. \{(a)\mdownarrow{} {}\mRightarrow{} (b)\mdownarrow{}\} supposing a \mleq{} b
Date html generated:
2017_02_20-AM-10_54_53
Last ObjectModification:
2017_01_26-PM-00_14_26
Theory : general
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