Nuprl Lemma : dl-lt_functionality
∀x,y,x',y':dl-Obj(). ((↑dlo_eq(x;x')) ⇒ (↑dlo_eq(y;y')) ⇒ x ≤ y = x' ≤ y')
Proof
Definitions occuring in Statement :
dlo_le: a ≤ b,
dlo_eq: dlo_eq(a;b),
dl-Obj: dl-Obj(),
assert: ↑b,
bool: 𝔹,
all: ∀x:A. B[x],
implies: P ⇒ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
iff: P ⇐⇒ Q,
and: P ∧ Q,
squash: ↓T,
uall: ∀[x:A]. B[x],
true: True
Lemmas referenced :
assert-dlo_eq,
dlo_le_wf,
istype-assert,
dlo_eq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
productElimination,
independent_functionElimination,
applyEquality,
lambdaEquality_alt,
imageElimination,
isectElimination,
because_Cache,
natural_numberEquality,
sqequalRule,
imageMemberEquality,
baseClosed
Latex:
\mforall{}x,y,x',y':dl-Obj(). ((\muparrow{}dlo\_eq(x;x')) {}\mRightarrow{} (\muparrow{}dlo\_eq(y;y')) {}\mRightarrow{} x \mleq{} y = x' \mleq{} y')
Date html generated:
2019_10_15-AM-11_44_06
Last ObjectModification:
2019_04_11-PM-02_12_34
Theory : dynamic!logic
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