Nuprl Lemma : int_formula_prop_le_lemma
∀y,x,f:Top. (int_formula_prop(f;x "≤" y) ~ int_term_value(f;x) ≤ int_term_value(f;y))
Proof
Definitions occuring in Statement :
int_formula_prop: int_formula_prop(f;fmla),
intformle: left "≤" right,
int_term_value: int_term_value(f;t),
top: Top,
le: A ≤ B,
all: ∀x:A. B[x],
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
int_formula_prop: int_formula_prop(f;fmla),
intformle: left "≤" right,
int_formula_ind: int_formula_ind
Lemmas referenced :
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
hypothesis,
lemma_by_obid,
sqequalRule
Latex:
\mforall{}y,x,f:Top. (int\_formula\_prop(f;x "\mleq{}" y) \msim{} int\_term\_value(f;x) \mleq{} int\_term\_value(f;y))
Date html generated:
2016_05_14-AM-07_07_34
Last ObjectModification:
2015_12_26-PM-01_08_37
Theory : omega
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